Name: ________________________ Class: ___________________ Date: __________ ID: A 1 Geometry Module 5 Unit 2 Practice Exam Short Answer Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 1. mO 123 2. mP 26 In the figure, PA and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to scale. 3. For mAOC = 65, find mPOB.
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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Geometry Module 5 Unit 2 Practice Exam
Short Answer
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)
1. mO 123
2. mP 26
In the figure, PA
and PB
are tangent to circle O and PD
bisects BPA. The figure is not drawn to scale.
3. For mAOC = 65, find mPOB.
Name: ________________________ ID: A
2
4. For mAOC = 56, find mBPO.
5. AB is tangent to O. If AO 24 and BC 50, what is AB?
The diagram is not to scale.
6. A satellite is 9,400 miles from the horizon of Earth. Earth’s radius is about 4,000 miles. Find the approximate distance the satellite is from the Earth’s surface.The diagram is not to scale.
Name: ________________________ ID: A
3
7. BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 11, BC = 30, and DC = 2. Find AD to the nearest tenth.
8. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 29 inches. The radius of the larger gear is 19 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale.
9. AB is tangent to circle O at B. Find the length of the radius r for AB = 6 and AO = 11.5. Round to the nearest tenth if necessary. The diagram is not to scale.
Name: ________________________ ID: A
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10. Pentagon RSTUV is circumscribed about a circle. Solve for x for RS = 13, ST = 5, TU = 8, UV = 13, and VR = 14. The figure is not drawn to scale.
11. JK , KL, and LJ are all tangent to O (not drawn to scale). JA = 9, AL = 9, and CK = 8. Find the perimeter of JKL.
12. NA PA, MO NA, RO PA, MO = 3 ftWhat is PO?
Name: ________________________ ID: A
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13. BZ FZ, BZ CA, FZ DC , DF = 50 in.What is BC?
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.
14.
15.
Name: ________________________ ID: A
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16.
17. FG OP, RS OQ , FG = 24, RS = 35, OP = 13
Name: ________________________ ID: A
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Use the diagram. AB is a diameter, and AB CD. The figure is not drawn to scale.
18. Find m BD for m AC = 40.
19. WZ and XR are diameters. Find the measure of ZWX . (The figure is not drawn to scale.)
Name: ________________________ ID: A
8
20. The radius of circle O is 17, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.)
ID: A
1
Geometry Module 5 Unit 2 Practice ExamAnswer Section
SHORT ANSWER
1. ANS: 57
PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle | point of tangency | properties of tangents | central angleDOK: DOK 1
2. ANS: 64
PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: tangent to a circle | point of tangency | angle measure | properties of tangents | central angleDOK: DOK 1
3. ANS: 65
PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: properties of tangents | tangent to a circle | Tangent Theorem DOK: DOK 2
4. ANS: 34
PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 1 Finding Angle Measures KEY: properties of tangents | tangent to a circle | Tangent Theorem DOK: DOK 2
ID: A
2
5. ANS: 70
PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 2 Finding DistanceKEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean TheoremDOK: DOK 2
6. ANS: 6,216 miles
PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 2 Finding DistanceKEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean TheoremDOK: DOK 2
7. ANS: 31.3
PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 2 Finding DistanceKEY: tangent to a circle | point of tangency | properties of tangents | Pythagorean TheoremDOK: DOK 2
8. ANS: 11.5 inches
PTS: 1 DIF: L4 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 3 Finding a RadiusKEY: word problem | tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem DOK: DOK 2
9. ANS: 9.8
PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 3 Finding a RadiusKEY: tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean TheoremDOK: DOK 2
10. ANS: 8.5
PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 5 Circles Inscribed in Polygons KEY: properties of tangents | tangent to a circle | pentagon DOK: DOK 2
ID: A
3
11. ANS: 52
PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: 12-1.1 Use properties of a tangent to a circle STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-1 Problem 5 Circles Inscribed in Polygons KEY: properties of tangents | tangent to a circle | triangle DOK: DOK 2
12. ANS: 1.5 ft
PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle | radius | chord | congruent chords | bisected chords DOK: DOK 1
13. ANS: 50 in.
PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 2 Finding the Length of a Chord KEY: circle | radius | chord | congruent chords | bisected chords DOK: DOK 1
14. ANS: 20
PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 3 Using Diameters and Chords KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2
15. ANS: 10.8
PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 3 Using Diameters and Chords KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2
ID: A
4
16. ANS: 65
PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | central angle | congruent arcsDOK: DOK 1
17. ANS: 2.6
PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: circle | radius | chord | congruent chords | right triangle | Pythagorean TheoremDOK: DOK 3
18. ANS: 140
PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | chord-arc relationship | diameter | chord | perpendicular | angle measure | circle | right triangle | perpendicular bisector DOK: DOK 2
19. ANS: 221
PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: 12-2.1 Use congruent chords, arcs, and central angles STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: arc | central angle | congruent arcs | arc measure | arc addition | diameterDOK: DOK 1
20. ANS: 21.9
PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: 12-2.2 Use perpendicular bisectors to chords STA: MA.912.G.6.1| MA.912.G.6.2| MA.912.G.6.3 TOP: 12-2 Problem 4 Finding Measures in a Circle KEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2
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